The generator matrix

 1  0  0  0  1  1  1  1  1 (a+1)X  0  1  1  1  1  1 aX  X  1  1 aX  1  1  1  1 (a+1)X  1 (a+1)X  1  1  1  1  1 aX  1  1 (a+1)X  X  1  1  1 (a+1)X  1  1  1  1  1  1  1  X  1  1  1  1 aX  1  0  1  1  1  1  1
 0  1  0  0  X aX  X (a+1)X (a+1)X  1  1 (a+1)X+1 X+a aX+a X+1 aX+1  1  X  1 (a+1)X+a  1 (a+1)X+a aX+1  a aX+a  1 X+a  1 X+1 X+1 (a+1)X+a+1 (a+1)X  1  1 X+a+1 a+1  1  1 a+1  1 (a+1)X+a  X (a+1)X+a  1  a  X aX+a (a+1)X+a+1 (a+1)X  1 aX+a+1 aX+1 X+1  0 (a+1)X  X  1 aX+a+1 X+a+1 (a+1)X  1  a
 0  0  1  0 (a+1)X+1 (a+1)X  a (a+1)X  0 aX  X X+a+1 aX+a+1 X+1 X+1 X+a X+a  1 (a+1)X aX+a a+1 X+a+1 aX+a+1 X+a a+1 a+1 a+1 X+1 aX+1 (a+1)X aX+a+1 X+a+1  0 (a+1)X+a+1 X+a (a+1)X+a (a+1)X+1  a (a+1)X+1 aX+a X+1  1  X aX+a+1  a  1  X X+a+1 a+1  1  0  X (a+1)X+1 (a+1)X+1  1 (a+1)X aX+a  X aX X+a a+1 aX+a+1
 0  0  0  1 a+1  1 X+a+1  a aX+a+1  1 (a+1)X+a (a+1)X+a+1 (a+1)X+a+1 X+1 (a+1)X+1 X+1 aX+a+1 X+a+1 (a+1)X+a  1 X+1 X+a (a+1)X+1 X+a (a+1)X+1 (a+1)X+a+1  X X+a+1  X X+a+1  0 (a+1)X+a X+1 aX+a (a+1)X+a+1 aX (a+1)X+1 aX  a  X aX+a aX+1 aX+1 (a+1)X aX  X aX+a+1  1 aX aX+a aX+a X+1 (a+1)X+a+1 X+1 X+a+1 (a+1)X+1 X+a  X X+a+1 aX+a  a (a+1)X+1

generates a code of length 62 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 171.

Homogenous weight enumerator: w(x)=1x^0+960x^171+564x^172+4380x^175+1617x^176+6864x^179+2796x^180+9192x^183+2880x^184+10224x^187+3564x^188+9804x^191+2925x^192+5616x^195+1668x^196+1872x^199+312x^200+240x^203+48x^204+9x^208

The gray image is a linear code over GF(4) with n=248, k=8 and d=171.
This code was found by Heurico 1.16 in 18.1 seconds.